The Best Linear Unbiased Estimator for Continuation of a Function

We show how to construct the best linear unbiased predictor (BLUP) for the continuation of a curve in a spline-function model. We assume that the entire curve is drawn from some smooth random process and that the curve is given up to some cut point. We demonstrate how to compute the BLUP efficiently. Confidence bands for the BLUP are discussed. Finally, we apply the proposed BLUP to real-world call center data. Specifically, we forecast the continuation of both the call arrival counts and the workload process at the call center of a commercial bank.

💡 Research Summary

The paper presents a rigorous framework for predicting the continuation of a smooth function when only a truncated portion of the curve is observed. The authors assume that the entire curve is a realization of a smooth stochastic process, specifically a Gaussian process with mean function μ(t) and covariance function K(s, t). Within the observed interval